Finite Group Databasebeta

← C31×#9926 #21466685

Subgroups — C31×#9926 #21466685

Order 7936.

734 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#483C211yesmaximal, characteristic, complemented
2C31×#2626C211yesmaximal, characteristic
3C2×C31×#397C211yesmaximal, characteristic
4C31×#1823C211yesmaximal, characteristic, complemented
5C2×C31×#328C211yesmaximal, characteristic, complemented
6C2×C31×#323C211yesmaximal, characteristic
7C31×#1294C211yesmaximal, characteristic, complemented
8C2×C31×C22⋊Q8C2211yescharacteristic
9C22×C4⋊C4×C31C2211yescharacteristic
10C22×C22⋊C4×C31—21no—
11C22×C22⋊C4×C31C2211yescharacteristic
12C31×#483—22no—
13C31×#483—22no—
14C2×C31×#106—21no—
15C2×C31×#103—21no—
16C2×C31×C22⋊C8C2211yescharacteristic
17C2×C31×C22⋊C8C2211yescharacteristic
18C31×#399—21no—
19C31×#397—22no—
20C31×#397—22no—
21C31×#396—22no—
22C31×#393—21no—
23C31×#385—21no—
24C31×#380C2211yescharacteristic
25C31×#379—21no—
26C2×C31×#95—21no—
27C2×C31×#95C2211yescharacteristic
28C31×#340—22no—
29C31×#328—22no—
30C31×#323—22no—
31C25×C31D411yescharacteristic
32C22×Q8×C31D411yescharacteristic
33C23×C4×C31—21no—
34C23×C4×C31—21no—
35C23×C4×C31D411yescharacteristic
36C23×C4×C31C2311yescharacteristic
37C22×C8×C31—21no—
38C22×C8×C31—21no—
39C31×C22⋊Q8—21no—
40C31×C22⋊Q8—21no—
41C31×C22⋊Q8—21no—
42C31×C22⋊Q8—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31D412yes—
51C2×C4⋊C4×C31D411yescharacteristic
52C2×C4⋊C4×C31D412yes—
53C2×C22⋊C4×C31—24no—
54C2×C22⋊C4×C31—21no—
55C2×C22⋊C4×C31—21no—
56C2×C22⋊C4×C31—21no—
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—21no—
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31—42no—
65C2×C22⋊C4×C31—42no—
66C31×#106—24no—
67C31×#103—24no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8D412yes—
72C31×#95—22no—
73C31×#95—24no—
74C31×#95—21no—
75C31×#95—21no—
76C31×#95D412yes—
77C24×C31—21no—
78C24×C31—21no—
79C24×C31—21no—
80C24×C31—21no—
81C24×C31—21no—
82C24×C31—21no—
83C24×C31—42no—
84C24×C31—42no—
85C24×C31SD1612yes—
86C24×C31C2×D411yescharacteristic
87C2×Q8×C31—21no—
88C2×Q8×C31—21no—
89C2×Q8×C31—42no—
90C22×C4×C31—21no—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—22no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—42no—
99C22×C4×C31—42no—
100C22×C4×C31—42no—
101C22×C4×C31—42no—
102C22×C4×C31—41no—
103C22×C4×C31—41no—
104C22×C4×C31—41no—
105C22×C4×C31—41no—
106C22×C4×C31—41no—
107C22×C4×C31—41no—
108C22×C4×C31—41no—
109C22×C4×C31—41no—
110C22×C4×C31C2×D411yescharacteristic
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31C2×D411yescharacteristic
113C22×C4×C31C2×D411yescharacteristic
114C22×C4×C31C2×D411yescharacteristic
115C22×C4×C31#4111yescharacteristic
116C2×C8×C31—22no—
117C2×C8×C31—42no—
118C2×C8×C31—42no—
119C2×C8×C31—41no—
120C4⋊C4×C31—22no—
121C4⋊C4×C31—21no—
122C4⋊C4×C31—22no—
123C4⋊C4×C31—21no—
124C4⋊C4×C31—42no—
125C4⋊C4×C31—41no—
126C4⋊C4×C31—41no—
127C4⋊C4×C31—41no—
128C4⋊C4×C31—41no—
129C4⋊C4×C31—82no—
130C22⋊C4×C31—48no—
131C22⋊C4×C31—41no—
132C22⋊C4×C31—41no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—41no—
135C22⋊C4×C31—41no—
136C22⋊C4×C31—41no—
137C22⋊C4×C31—41no—
138C22⋊C4×C31—41no—
139C22⋊C4×C31—82no—
140C22⋊C4×C31—82no—
141#9926C3111yesmaximal, characteristic, direct product factor, Sylow
142C23×C31—22no—
143C23×C31—22no—
144C23×C31—22no—
145C23×C31—22no—
146C23×C31—22no—
147C23×C31—44no—
148C23×C31—44no—
149C23×C31—42no—
150C23×C31—42no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31—41no—
154C23×C31—42no—
155C23×C31—42no—
156C23×C31—41no—
157C23×C31—82no—
158C23×C31—82no—
159C23×C31—81no—
160C23×C31—81no—
161C23×C31#12011yescharacteristic
162C23×C31#12011yescharacteristic
163C23×C31#12111yescharacteristic
164C23×C31C2×SD1611yescharacteristic
165C23×C31#13511yescharacteristic
166C23×C31AGL(1,ℤ/8)11yescharacteristic
167C23×C31#13711yescharacteristic
168Q8×C31—42no—
169Q8×C31—81no—
170C2×C4×C31—22no—
171C2×C4×C31—22no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—41no—
176C2×C4×C31—42no—
177C2×C4×C31—42no—
178C2×C4×C31—42no—
179C2×C4×C31—41no—
180C2×C4×C31—41no—
181C2×C4×C31—41no—
182C2×C4×C31—42no—
183C2×C4×C31—42no—
184C2×C4×C31—42no—
185C2×C4×C31—42no—
186C2×C4×C31—42no—
187C2×C4×C31—42no—
188C2×C4×C31—42no—
189C2×C4×C31—42no—
190C2×C4×C31—42no—
191C2×C4×C31—42no—
192C2×C4×C31—82no—
193C2×C4×C31—82no—
194C2×C4×C31—81no—
195C2×C4×C31—81no—
196C2×C4×C31—81no—
197C2×C4×C31—81no—
198C2×C4×C31—81no—
199C2×C4×C31#12011yescharacteristic
200C2×C4×C31#12111yescharacteristic
201C2×C4×C31#12111yescharacteristic
202C2×C4×C31#12711yescharacteristic
203C8×C31—42no—
204C8×C31—81no—
205C2×#483C2×C3111yescharacteristic, complemented
206#2626C2×C3111yescharacteristic
207C2×#397C2×C3111yescharacteristic
208#1823C2×C3111yescharacteristic, complemented
209C2×#328C2×C3111yescharacteristic, complemented
210C2×#323C2×C3111yescharacteristic
211#1294C2×C3111yescharacteristic, complemented
212C22×C31—22no—
213C22×C31—22no—
214C22×C31—22no—
215C22×C31—22no—
216C22×C31—21no—
217C22×C31—21no—
218C22×C31—21no—
219C22×C31—21no—
220C22×C31—44no—
221C22×C31—44no—
222C22×C31—42no—
223C22×C31—82no—
224C22×C31—82no—
225C22×C31—82no—
226C22×C31—82no—
227C22×C31—81no—
228C22×C31—81no—
229C22×C31#39211yescharacteristic
230C22×C31#44811yescharacteristic
231C22×C31#44911yescharacteristic
232C22×C31#45011yescharacteristic
233C22×C31#45211yescharacteristic
234C22×C31#45512yes—
235C22×C31#45812yes—
236C22×C31#46511yescharacteristic
237C22×C31#46811yescharacteristic
238C4×C31—21no—
239C4×C31—21no—
240C4×C31—21no—
241C4×C31—21no—
242C4×C31—82no—
243C4×C31—82no—
244C4×C31—82no—
245C4×C31—81no—
246C4×C31—81no—
247C4×C31—81no—
248C2×C22⋊Q8C22×C3111yescharacteristic
249C22×C4⋊C4C22×C3111yescharacteristic
250C22×C22⋊C4—21no—
251C22×C22⋊C4C22×C3111yescharacteristic
252#483—22no—
253#483—22no—
254C2×#106—21no—
255C2×#103—21no—
256C2×C22⋊C8C22×C3111yescharacteristic
257C2×C22⋊C8C22×C3111yescharacteristic
258#399—21no—
259#397—22no—
260#397—22no—
261#396—22no—
262#393—21no—
263#385—21no—
264#380C22×C3111yescharacteristic
265#379—21no—
266C2×#95—21no—
267C2×#95C22×C3111yescharacteristic
268#340—22no—
269#328—22no—
270#323—22no—
271C2×C31—21no—
272C2×C31—21no—
273C2×C31—21no—
274C2×C31—21no—
275C2×C31—82no—
276C2×C31#160812yes—
277C2×C31#161212yes—
278C2×C31#200011yescharacteristic
279C2×C31#200411yescharacteristic
280C2×C31#202211yescharacteristic
281C25D4×C3111yescharacteristic
282C22×Q8D4×C3111yescharacteristic
283C23×C4—21no—
284C23×C4—21no—
285C23×C4D4×C3111yescharacteristic
286C23×C4C23×C3111yescharacteristic
287C22×C8—21no—
288C22×C8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4D4×C3112yes—
301C2×C4⋊C4D4×C3111yescharacteristic
302C2×C4⋊C4D4×C3112yes—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316#106—24no—
317#103—24no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8D4×C3112yes—
322#95—24no—
323#95—22no—
324#95—21no—
325#95—21no—
326#95D4×C3112yes—
327C31#992611yescharacteristic, direct product factor, Sylow
328C24—21no—
329C24—21no—
330C24—21no—
331C24—21no—
332C24—21no—
333C24—21no—
334C24—42no—
335C24—42no—
336C24SD16×C3112yes—
337C24C2×D4×C3111yescharacteristic
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4C2×D4×C3111yescharacteristic
362C22×C4C2×D4×C3111yescharacteristic
363C22×C4C2×D4×C3111yescharacteristic
364C22×C4C2×D4×C3111yescharacteristic
365C22×C4C2×D4×C3111yescharacteristic
366C22×C4#41×C3111yescharacteristic
367C2×C8—22no—
368C2×C8—42no—
369C2×C8—42no—
370C2×C8—41no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—42no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—82no—
381C22⋊C4—48no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—82no—
391C22⋊C4—82no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—44no—
398C23—44no—
399C23—42no—
400C23—42no—
401C23—41no—
402C23—41no—
403C23—42no—
404C23—42no—
405C23—41no—
406C23—41no—
407C23—82no—
408C23—82no—
409C23—81no—
410C23—81no—
411C23C31×#12011yescharacteristic
412C23C31×#12011yescharacteristic
413C23C31×#12111yescharacteristic
414C23C2×SD16×C3111yescharacteristic
415C23C31×#13511yescharacteristic
416C23C31×AGL(1,ℤ/8)11yescharacteristic
417C23C31×#13711yescharacteristic
418Q8—42no—
419Q8—81no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4C31×#12011yescharacteristic
450C2×C4C31×#12111yescharacteristic
451C2×C4C31×#12111yescharacteristic
452C2×C4C31×#12711yescharacteristic
453C8—42no—
454C8—81no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—44no—
465C22—42no—
466C22—82no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—81no—
471C22—81no—
472C22C31×#39211yescharacteristic
473C22C31×#44811yescharacteristic
474C22C31×#44911yescharacteristic
475C22C31×#45011yescharacteristic
476C22C31×#45211yescharacteristic
477C22C31×#45512yes—
478C22C31×#45812yes—
479C22C31×#46511yescharacteristic
480C22C31×#46811yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—82no—
486C4—82no—
487C4—82no—
488C4—81no—
489C4—81no—
490C4—81no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—82no—
496C2C31×#160812yes—
497C2C31×#161212yes—
498C2C31×#200011yescharacteristic
499C2C31×#200411yescharacteristic
500C2C31×#202211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C31×#483C2semidirect
4. C31×#1823C2semidirect
5. C2×C31×#328C2semidirect
7. C31×#1294C2semidirect
141. #9926C31direct (N × H)
205. C2×#483C2×C31semidirect
208. #1823C2×C31semidirect
209. C2×#328C2×C31semidirect
211. #1294C2×C31semidirect
327. C31#9926direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C31×#4832
C31×#26262
C2×C31×#3972
C31×#18232
C2×C31×#3282
C2×C31×#3232
C31×#12942
#992631